Statistical Analysis of Saudi Arabia’s Environmental Sustainability Indicators using Log-Logistic Current Records

Abstract

Accurate modeling and prediction of atmospheric pressure are essential for climate monitoring, weather forecasting, and environmental sustainability planning. Motivated by the importance of analyzing atmospheric-pressure variability in Riyadh, Saudi Arabia, this paper develops a comprehensive statistical framework for upper and lower current records under theLog-Logistic distribution. New closed-form probability density and cumulative distribution functions are derived using recently established general current-record formulas. Joint and conditional density functions, moments, Shannon entropy, and extropy are also obtained. Maximum likelihood and Bayesian methods are proposed to estimate the unknown parameters, while Bayesian posterior predictive procedures are developed to predict future current records. Since the resulting likelihood equations have no closed-form solutions, numerical optimization and Markov Chain Monte Carlo algorithms are employed for estimation andprediction. A Monte Carlo simulation study demonstrates that estimation accuracy improves as the number of current records increases, with the Bayesian approach providing slightly more stable estimates. The proposed methodology is applied to daily atmospheric-pressure observations from Riyadh, where the Log-Logistic distribution provides an excellent fit andyields reliable predictions of future pressure extremes. The proposed framework offers an effective tool for modeling environmental extremes and supporting climate and environmental sustainability studies.